Minimal Electromagnetic Currents and Commutation Relations

Abstract

It is pointed out that within the quark model the equal-time commutation relations of currents provide us with a test of minimal electromagnetic interaction of the hadrons. When compared with experiment, the modifications of the Cabibbo-Radicati and Drell-Hearn sum rules resulting from nonminimal interactions may possibly fix the magnitudes of the isoscalar and the isovector Pauli interactions.

Updated resonance photodecay amplitudes to 2 GeV

“…[40]), the results presented here should provide a useful test for the form proposed by Chang and Liang [39]. While the isoscalar FFR sum rule would likely provide the most sensitive check on any such contribution, the phenomenological evaluation of the associated integral is not yet sufficiently stable for more than an order-of-magnitude test.…”

“…[40] mentioned in passing that a similar procedure could be used to determine modifications to the FFR sum rule.…”

Current Algebra and Unitarity

“…Motivated by the hard-pion philosophy one can assume that Imr^s) =0 for 4^ s ^ s 0 . Then, if Imt x c (s) = 0 and ImT^s) = 0 for 4 < s ^ s 0 , from (5a) and (6b), ^=0, which is a weak form of the so-called 8 fd?n 2 pV(m 2 )/m 2 = -2F v 2 m [Note that we have made no appeal to meson dom-inance, or even assumed the existence of any resonances,,] If we adopt this approximation, the absence of spurious poles in A 7 (s), computed from (8) and (11), suggests f 1 =0. Now evaluate Eq.…”

“…The equations implied by (8) are readily found to be 2^v.. a2s * + /> fe <? V .. a2S = 0, a ra2S .p0 ai ... a2s + 2mx v .. a2S _/=O, which, upon inclusion of minimal coupling, yield as the equation of motion for the independent components <p…”

The Gerasimov - Drell - Hearn sum rule and nucleon structure

“…where U (pS) is the nucleon spinor, F 1,..., 8 are invariant amplitudes that are otherwise independent if gauge invariance is not required. The Ward identity Eq.…”